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Significant Figures and Scientific Notations

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Significant Figures and Scientific Notations

Examples and Problems

Rules for Counting Significant Figures

1. Nonzero integers always count as significant figures.

2. Zeros: There are three classes of zeroes.

- Leading zeroes precede all the nonzero digits and DO NOT count as
- significant figures. Example: 0.0025 has ____ significant figures.
- Captive zeroes are zeroes between nonzero numbers. These always
- count as significant figures. Example: 1.008 has ____ significant figures.
- Trailing zeroes are zeroes at the right end of the number.
- Trailing zeroes are only significant if the number contains a decimal point.
- Example: 1.00 x 102 has ____ significant figures.
- Trailing zeroes are not significant if the number does not contain a decimal
- point. Example: 100 has ____ significant figure.
- Exact numbers, which can arise from counting or definitions such as 1 in
- = 2.54 cm, never limit the number of significant figures in a calculation.

2

4

3

1

Ohn-Sabatello, Morlan, Knoespel, Fast Track to a 5 Preparing for the AP Chemistry Examination2006, page 53

Leading zeros are not significant.

Leading zero

– three significant figures

0.421

Captive zeros are significant.

Captive zero

4012

– four significant figures

Trailing zeros are significant.

Trailing zero

114.20

– five significant figures

- Counting Sig Figs
- Count all numbers EXCEPT:
- Leading zeros -- 0.0025
- Trailing zeros without a decimal point -- 2,500

- Count all numbers EXCEPT:

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

3 SF

- Calculating with Sig Figs
- Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer.

(13.91g/cm3)(23.3cm3) = 324.103g

4 SF

3 SF

324g

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

- Calculating with Sig Figs (con’t)
- Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

224 g

+ 130 g

354 g

224 g

+ 130 g

354 g

3.75 mL

+ 4.1 mL

7.85 mL

3.75 mL

+ 4.1 mL

7.85 mL

350 g

7.9 mL

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

- Calculating with Sig Figs (con’t)
- Exact Numbers do not limit the # of sig figs in the answer.
- Counting numbers: 12 students
- Exact conversions: 1 m = 100 cm
- “1” in any conversion: 1 in = 2.54 cm

- Exact Numbers do not limit the # of sig figs in the answer.

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

1. (15.30 g) ÷ (6.4 mL)

2.4 g/mL

2 SF

Practice Problems

4 SF

2 SF

= 2.390625 g/mL

2. 18.9g

- 0.84 g

18.1 g

18.06 g

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

65,000 kg 6.5 × 104 kg

- Converting into scientific notation:
- Move decimal until there’s 1 digit to its left. Places moved = exponent.
- Large # (>1) positive exponentSmall # (<1) negative exponent
- Only include sig. figs.

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

3. 2,400,000 g

4. 0.00256 kg

5. 7 10-5 km

6.6.2 104 mm

Practice Problems

2.4 106 g

2.56 10-3 kg

0.00007 km

62,000 mm

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem

EXE

EXP

EXP

ENTER

EE

EE

- Calculating with scientific notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

Type on your calculator:

5.44

7

8.1

4

÷

= 671.6049383

= 670 g/mol

= 6.7 × 102 g/mol

Courtesy Christy Johannesson www.nisd.net/communicationsarts/pages/chem